Question

If $A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$ and $B = \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix}$ are arbitrary vectors in $\mathbb{R}^{2 \times 2}$, then the mapping $(A, B) = a_{11}b_{11} + a_{12}b_{12} + a_{21}b_{21} + a_{22}b_{22}$ defines an inner product in $\mathbb{R}^{2 \times 2}$. Use this inner product to determine $(A, B)$, $||A||$, $||B||$, and the angle $\alpha_{A, B}$ between $A$ and $B$ for $A = \begin{bmatrix} -4 & -4 \\ 4 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -5 & -1 \\ -3 & -5 \end{bmatrix}$. $(A, B) = ||A|| = ||B|| = $\alpha_{A, B} =

          If
$A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$ and $B = \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix}$
are arbitrary vectors in $\mathbb{R}^{2 \times 2}$, then the mapping
$(A, B) = a_{11}b_{11} + a_{12}b_{12} + a_{21}b_{21} + a_{22}b_{22}$
defines an inner product in $\mathbb{R}^{2 \times 2}$. Use this inner product to determine $(A, B)$, $||A||$, $||B||$, and the angle $\alpha_{A, B}$
between $A$ and $B$ for
$A = \begin{bmatrix} -4 & -4 \\ 4 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -5 & -1 \\ -3 & -5 \end{bmatrix}$.
$(A, B) = 
||A|| = 
||B|| = 
$\alpha_{A, B} =

If
A =
< b m a t r i x > and B =
< b m a t r i x >
are arbitrary vectors in ℝ^2 × 2, then the mapping
(A, B) = a11b11 + a12b12 + a21b21 + a22b22
defines an inner product in ℝ^2 × 2. Use this inner product to determine (A, B), ||A||, ||B||, and the angle αA, B
between A and B for
A =
< b m a t r i x > and B =
< b m a t r i x >.
(A, B) =
||A|| =
||B|| =αA, B =

Added by Arthur R.

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